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arXiv · 2104.09881

Brouwer degree for Kazdan-Warner equations on a connected finite graph

Linlin Sun·Liuquan Wang
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Abstract

We study Kazdan-Warner equations on a connected finite graph via the method of the degree theory. Firstly, we prove that all solutions to the Kazdan-Warner equation with nonzero prescribed function are uniformly bounded and the Brouwer degree is well defined. Secondly, we compute the Brouwer degree case by case. As consequences, we give new proofs of some known existence results for the Kazdan-Warner equation on a connected finite graph.

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BibTeXRIS

Linlin Sun, Liuquan Wang. 2021-04-20. Brouwer degree for Kazdan-Warner equations on a connected finite graph. https://arxiv.org/abs/2104.09881

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